geometric quantization higher geometric quantization
geometry of physics: Lagrangians and Action functionals + Geometric Quantization
prequantum circle n-bundle = extended Lagrangian
prequantum 1-bundle = prequantum circle bundle, regularcontact manifold,prequantum line bundle = lift of symplectic form to differential cohomology
The concept of coherent state in quantum mechanics/quantum physics may be formalized in the context of geometric quantization, The original definition is due to (Rawnsley 77), further developments include (Kirwin 07).
The original reference that interpreted coherent states in geometric quantization over Kähler manifolds is
A review and further developments of these considerations are in
Generalization to non-Kähler symplectic manifolds is in
See also
Anatol Odzijewicz, Coherent state method in geometric quantization, in Twenty Years of Bialowiez: a mathematical anthology, Aspects of Differential Geometric Methods in Physics_ (pp 47-78) , World Sci. Monogr. Ser. Math. 8 (2005); Coherent states and geometric quantization, Comm. Math. Phys. 150 (1992), no. 2, 385–413 doi 94c:58077
Brian Charles Hall, Geometric quantization and the generalized Segal–Bargmann transform for Lie groups of compact type, Comm. Math. Phys., 226:233–268, 2002. doi
D. J. Rowe, Coherent states, induced representations, geometric quantization, and their vector coherent state extensions, Symmetry in physics, 177–188, CRM Proc. Lecture Notes 34, Amer. Math. Soc. 2004. MR2005a:81100
C. Florentino, P. Matias, J. Mourão, J. P. Nunes, Geometric quantization, complex structures and the coherent state transform, J. Funct. Anal. 221(2):303–322, 2005 MR2005m:53179 doi